He spent only one season in the Mets' farm system AA Williamsport, PA before making the team out of Spring training, 1965. He made his major league debut as a pinch hitter in the 1965 season opener, and lined out in his only at-bat.[1] He pinch hit, again, in the second game of the season, this time, hitting an 11th inning home run (the Mets still lost, as the Houston Astros scored four runs in the top of the inning).[2] He homered again, in his first at-bat on April 18, giving him two home runs in his first four Major League at bats.

He had 15 home runs by the All-Star break, the most by a Mets rookie ever in the first half, ahead of Benny Agbayani (11; in 1999) and Ike Davis (11; in 2010).[3] He commented during a TV interview that he loved hitting fastballs. From that point forward, he began seeing a lot more breaking balls, and only hit four more for the rest of the season. Still, his 19 home runs stood as a Mets rookie record until Darryl Strawberry hit 26 in 1983. His fielding percentage his rookie year was a below-league-average .947, however, he had nine outfield assists.

Swoboda wore number 14 as a rookie in 1965. When the Mets acquired third basemanKen Boyer from the St. Louis Cardinals prior to the start of the 1966 season, they granted him number 14, as he'd worn it in St. Louis. Swoboda wore number 17 briefly during Spring training in 1966, then switched to number 4. His home run drought continued through the 1966 season, when he hit only eight home runs and batted .222, with fifty runs batted in.

During his early years with the Mets, he acquired the nickname "Rocky" as a result of his less-than-reliable fielding. Although he possessed a strong, accurate throwing arm, a fly ball hit in his direction was, by no means, a sure out. After having spent most of his time in left field his first two seasons with the Mets, Swoboda was shifted to first baseman in 1967 to make room for newly acquired Tommy Davis in left. Swoboda's fielding at first was no better, and he was soon shifted to right field. Offensively, he had perhaps his best season, hitting .281 with thirteen home runs and 53 RBIs. He led the Mets with six triples and a career high 59 RBIs in 1968, and also had a career high fourteen outfield assists.

By May 21, 1969, the Mets won their third game in a row for a .500 winning percentage 36 games into the season for the first time in franchise history. This was followed by a five-game losing streak that saw the Mets fall into fourth place in the newly aligned National League East.

The Mets then went on an eleven-game winning streak that brought them back into second place, seven games back of the Chicago Cubs. On September 10 the Mets swept a double header against the Montreal Expos. Coupled with a loss by the Cubs, the Mets jump into first place for the first time in franchise history. On September 13, Swoboda hit a grand slam against the Pittsburgh Pirates to propel the Mets to a 5–2 victory.[4] Two days later, the St. Louis Cardinals' Steve Carlton struck out a record nineteen Mets batters in a losing effort, as the Mets defeated the Cards 4–3 at Busch Stadium on a pair of two run home runs by Swoboda.[5] On September 24, facing Carlton and the Cardinals, again - only this time at Shea Stadium, the New York Mets clinched the NL East as Donn Clendenon hit two home runs in a 6–0 Mets victory.[6] The Mets won 39 of their last 50 games, and finished the season with 100 wins against 62 losses, eight games over the second place Cubs.

A photograph of Swoboda, stretched almost horizontally, just inches off the ground, became an iconic image for Mets fans. The Right Field entrance gate of Citi Field, the current ballpark of the Mets, features a metal silhouette of a baseball player making a diving catch similar to the one Swoboda made during the 1969 Series.[8]

In March 1971, Swoboda and minor leaguer Rich Hacker were traded to the Montreal Expos in exchange for young outfielder Don Hahn. Three months later, the Expos traded Swoboda to the New York Yankees in exchange for outfielder Ron Woods. He was released by the Yankees at the end of 1973, and signed with the Atlanta Braves during Spring training of 1974. The Braves, however, released him on March 25, 1974, after which Swoboda retired from baseball. He attempted an unsuccessful comeback with the Mets during spring training in 1976.

Swoboda appeared as himself in a 1999 episode of Everybody Loves Raymond along with several other members of the 1969 Mets.[9] He is mostly remembered for his theatrical defensive gem during the 1969 World Series. In a guest column for the New York Daily News, Swoboda wrote, "I'm kidded, occasionally, by folks who wonder: 'How long are you going to keep living off of one catch?' My answer: 'How long have I got left?'"[10]